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Geometric control of particle manipulation in a two-dimensional fluid

Yizhar Or, Joris Vankerschaver UGent, Scott D Kelly, Richard M Murray and Jerrold E Marsden (2009) 2009 Joint 48th IEEE Conference on Decision and Control (CDC) and 28th Chinese Control Conference (CCC 2009). p.19-26
abstract
Manipulation of particles suspended in fluids is crucial for many applications, such as precision machining, chemical processes, bio-engineering, and self-feeding of microorganisms. In this paper, we study the problem of particle manipulation by cyclic fluid boundary excitations from a geometric-control viewpoint. We focus on the simplified problem of manipulating a single particle by generating controlled cyclic motion of a circular rigid body in a two-dimensional perfect fluid. We show that the drift in the particle location after one cyclic motion of the body can be interpreted as the geometric phase of a connection induced by the system's hydrodynamics. We then formulate the problem as a control system, and derive a geometric criterion for its nonlinear controllability. Moreover, by exploiting the geometric structure of the system, we explicitly construct a feedback-based gait that results in attraction of the particle towards the rigid body. We argue that our gait is robust and model-independent, and demonstrate it in both perfect fluid and Stokes fluid.
Please use this url to cite or link to this publication:
author
organization
year
type
conference (conferencePaper)
publication status
published
subject
keyword
feedback, controllability, flow control, hydrodynamics, nonlinear control systems, two-phase flow, geometric control, particle manipulation, cyclic fluid boundary excitations, controlled cyclic motion, circular rigid body, 2D perfect fluid, control system, nonlinear controllability, feedback-based gait, Stokes fluid
in
2009 Joint 48th IEEE Conference on Decision and Control (CDC) and 28th Chinese Control Conference (CCC 2009)
pages
19 - 26
publisher
IEEE
place of publication
Piscataway, NJ, USA
conference name
2009 Joint 48th IEEE Conference on Decision and Control (CDC) and 28th Chinese Control Conference (CCC 2009)
conference location
Shanghai, PR China
conference start
2009-12-16
conference end
2009-12-18
Web of Science type
Conference Paper
Web of Science id
11148504
ISBN
9781424438716
DOI
10.1109/CDC.2009.5399499
language
English
UGent publication?
yes
classification
C1
copyright statement
I have transferred the copyright for this publication to the publisher
id
1073593
handle
http://hdl.handle.net/1854/LU-1073593
date created
2010-11-15 01:58:07
date last changed
2017-01-02 09:52:45
@inproceedings{1073593,
  abstract     = {Manipulation of particles suspended in fluids is crucial for many applications, such as precision machining, chemical processes, bio-engineering, and self-feeding of microorganisms. In this paper, we study the problem of particle manipulation by cyclic fluid boundary excitations from a geometric-control viewpoint. We focus on the simplified problem of manipulating a single particle by generating controlled cyclic motion of a circular rigid body in a two-dimensional perfect fluid. We show that the drift in the particle location after one cyclic motion of the body can be interpreted as the geometric phase of a connection induced by the system's hydrodynamics. We then formulate the problem as a control system, and derive a geometric criterion for its nonlinear controllability. Moreover, by exploiting the geometric structure of the system, we explicitly construct a feedback-based gait that results in attraction of the particle towards the rigid body. We argue that our gait is robust and model-independent, and demonstrate it in both perfect fluid and Stokes fluid.},
  author       = {Or, Yizhar and Vankerschaver, Joris and Kelly, Scott D and Murray, Richard M and Marsden, Jerrold E},
  booktitle    = {2009 Joint 48th IEEE Conference on Decision and Control (CDC) and 28th Chinese Control Conference (CCC 2009)},
  isbn         = {9781424438716},
  keyword      = {feedback,controllability,flow control,hydrodynamics,nonlinear control systems,two-phase flow,geometric control,particle manipulation,cyclic fluid boundary excitations,controlled cyclic motion,circular rigid body,2D perfect fluid,control system,nonlinear controllability,feedback-based gait,Stokes fluid},
  language     = {eng},
  location     = {Shanghai, PR China},
  pages        = {19--26},
  publisher    = {IEEE},
  title        = {Geometric control of particle manipulation in a two-dimensional fluid},
  url          = {http://dx.doi.org/10.1109/CDC.2009.5399499},
  year         = {2009},
}

Chicago
Or, Yizhar, Joris Vankerschaver, Scott D Kelly, Richard M Murray, and Jerrold E Marsden. 2009. “Geometric Control of Particle Manipulation in a Two-dimensional Fluid.” In 2009 Joint 48th IEEE Conference on Decision and Control (CDC) and 28th Chinese Control Conference (CCC 2009), 19–26. Piscataway, NJ, USA: IEEE.
APA
Or, Y., Vankerschaver, J., Kelly, S. D., Murray, R. M., & Marsden, J. E. (2009). Geometric control of particle manipulation in a two-dimensional fluid. 2009 Joint 48th IEEE Conference on Decision and Control (CDC) and 28th Chinese Control Conference (CCC 2009) (pp. 19–26). Presented at the 2009 Joint 48th IEEE Conference on Decision and Control (CDC) and 28th Chinese Control Conference (CCC 2009), Piscataway, NJ, USA: IEEE.
Vancouver
1.
Or Y, Vankerschaver J, Kelly SD, Murray RM, Marsden JE. Geometric control of particle manipulation in a two-dimensional fluid. 2009 Joint 48th IEEE Conference on Decision and Control (CDC) and 28th Chinese Control Conference (CCC 2009). Piscataway, NJ, USA: IEEE; 2009. p. 19–26.
MLA
Or, Yizhar, Joris Vankerschaver, Scott D Kelly, et al. “Geometric Control of Particle Manipulation in a Two-dimensional Fluid.” 2009 Joint 48th IEEE Conference on Decision and Control (CDC) and 28th Chinese Control Conference (CCC 2009). Piscataway, NJ, USA: IEEE, 2009. 19–26. Print.